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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 500 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 18 (d) 9
  3. 3.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 42 (c) 13 (d) 117
  4. 4.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 159 (c) 150 (d) 160
  5. 5.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 128 (c) 119 (d) 110
  6. 6.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 255 (d) 248
  7. 7.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 108 (d) 39
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  9. 9.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 72 (c) 82 (d) 90
  10. 10.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 393 (c) 394 (d) 334
  11. 11.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
  12. 12.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 171 (d) 19
  13. 13.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 285 (d) 268
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 13
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
  16. 16.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 420 (d) 421
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
  18. 18.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 303 (d) 274
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  20. 20.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 228 (d) 219
  21. 21.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 388 (c) 465 (d) 475
  22. 22.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 454 (c) 573 (d) 564
  23. 23.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 21 (c) 24 (d) 63
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 9 (c) 10 (d) 5
  25. 25.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 585 (c) 594 (d) 468
  26. 26.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 49 (c) 50 (d) 58
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 7 (c) 6 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  31. 31.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 450 (d) 451
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 15 (d) 5
  36. 36.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 153 (c) 17 (d) 51
  37. 37.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 378 (c) 387 (d) 330
  38. 38.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 45 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7

Answer key

  1. 7
  2. 19
  3. 39
  4. 159
  5. 119
  6. 264
  7. 36
  8. 4
  9. 81
  10. 393
  11. 60
  12. 57
  13. 294
  14. 14
  15. 20
  16. 420
  17. 18
  18. 303
  19. 4
  20. 228
  21. 474
  22. 573
  23. 21
  24. 9
  25. 594
  26. 49
  27. 3
  28. 7
  29. 3
  30. 8
  31. 450
  32. 6
  33. 15
  34. 9
  35. 16
  36. 51
  37. 387
  38. 15
  39. 2
  40. 8

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